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Journal articles on the topic 'Gevrey classes'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Hua, Chen, and Luigi Rodino. "Paradifferential calculus in Gevrey classes." Journal of Mathematics of Kyoto University 41, no. 1 (2001): 1–31. http://dx.doi.org/10.1215/kjm/1250517647.

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2

Kajitani, Kunihiko, and Seiichiro Wakabayashi. "Microhyperbolic operators in Gevrey classes." Publications of the Research Institute for Mathematical Sciences 25, no. 2 (1989): 169–221. http://dx.doi.org/10.2977/prims/1195173608.

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3

Colombini, Ferruccio, Nicola Orrù, and Giovanni Taglialatela. "Strong hyperbolicity in Gevrey classes." Journal of Differential Equations 272 (January 2021): 222–54. http://dx.doi.org/10.1016/j.jde.2020.09.033.

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4

Lascar, Bernard, and Richard Lascar. "FBI transforms in Gevrey classes." Journal d'Analyse Mathématique 72, no. 1 (December 1997): 105–25. http://dx.doi.org/10.1007/bf02843155.

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5

Calvo, Daniela, Alessandro Morando, and Luigi Rodino. "Inhomogeneous Gevrey classes and ultradistributions." Journal of Mathematical Analysis and Applications 297, no. 2 (September 2004): 720–39. http://dx.doi.org/10.1016/j.jmaa.2004.04.043.

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6

Calvo, Daniela, and María del Carmen Gómez-Collado. "On some generalizations of Gevrey classes." Mathematische Nachrichten 284, no. 7 (April 6, 2011): 856–74. http://dx.doi.org/10.1002/mana.200910840.

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7

Yonemura, Akiyoshi. "Newton polygons and formal Gevrey classes." Publications of the Research Institute for Mathematical Sciences 26, no. 1 (1990): 197–204. http://dx.doi.org/10.2977/prims/1195171666.

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8

Jannelli, Enrico. "Regularly hyperbolic systems and Gevrey classes." Annali di Matematica Pura ed Applicata 140, no. 1 (December 1985): 133–45. http://dx.doi.org/10.1007/bf01776846.

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9

Albanese, Angela A., Andrea Corli, and Luigi Rodino. "Hypoellipticity and Local Solvability in Gevrey Classes." Mathematische Nachrichten 242, no. 1 (July 2002): 5–16. http://dx.doi.org/10.1002/1522-2616(200207)242:1<5::aid-mana5>3.0.co;2-e.

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10

KAJITANI, Kunihiko, and Seiichiro WAKABAYASHI. "The hyperbolic mixed problem in Gevrey classes." Japanese journal of mathematics. New series 15, no. 2 (1989): 309–83. http://dx.doi.org/10.4099/math1924.15.309.

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11

CICOGNANI, M., and L. ZANGHIRATI. "NONLINEAR HYPERBOLIC CAUCHY PROBLEMS IN GEVREY CLASSES." Chinese Annals of Mathematics 22, no. 04 (October 2001): 417–26. http://dx.doi.org/10.1142/s0252959901000413.

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12

Oliaro, Alessandro, Luigi Rodino, and Patrik Wahlberg. "Almost periodic pseudodifferential operators and Gevrey classes." Annali di Matematica Pura ed Applicata 191, no. 4 (May 10, 2011): 725–60. http://dx.doi.org/10.1007/s10231-011-0203-4.

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13

Liess, Otto, and Luigi Rodino. "Fourier integral operators and inhomogeneous Gevrey classes." Annali di Matematica Pura ed Applicata 150, no. 1 (December 1988): 167–262. http://dx.doi.org/10.1007/bf01761469.

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14

Calvo, Daniela, and L. Rodino. "Inhomogeneous Gevrey ultradistributions and Cauchy problem." Bulletin: Classe des sciences mathematiques et natturalles 133, no. 31 (2006): 176–86. http://dx.doi.org/10.2298/bmat0631176c.

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After a short survey on Gevrey functions and ultradistributions, we present the inhomogeneous Gevrey ultradistributions introduced recently by the authors in collaboration with A. Morando, cf. [7]. Their definition depends on a given weight function ?, satisfying suitable hypotheses, according to Liess-Rodino [16]. As an application, we define (s, ?)-hyperbolic partial differential operators with constant coefficients (for s > 1), and prove for them the well-posedness of the Cauchy problem in the frame of the corresponding inhomogeneous ultradistributions. This sets in the dual spaces a similar result of Calvo [4] in the inhomogeneous Gevrey classes, that in turn extends a previous result of Larsson [14] for weakly hyperbolic operators in standard homogeneous Gevrey classes. AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.

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15

FUJITA, Keiko, and Mitsuo MORIMOTO. "Gevrey Classes on Compact Real Analytic Riemannian Manifolds." Tokyo Journal of Mathematics 18, no. 2 (December 1995): 341–55. http://dx.doi.org/10.3836/tjm/1270043467.

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16

Rodino, Luigi. "Pseudodifferential operators with multiple characteristics and Gevrey classes." Banach Center Publications 19, no. 1 (1987): 263–67. http://dx.doi.org/10.4064/-19-1-263-267.

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17

Schmets, Jean, and Manuel Valdivia. "The Zahorski theorem is valid in Gevrey classes." Fundamenta Mathematicae 151, no. 2 (1996): 149–66. http://dx.doi.org/10.4064/fm-151-2-149-166.

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18

Zanghirati, Luisa. "Pseudodifferential operators of infinite order and Gevrey classes." ANNALI DELL'UNIVERSITA' DI FERRARA 31, no. 1 (January 1985): 197–219. http://dx.doi.org/10.1007/bf02831766.

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19

Bendib, Elmostafa, and Hicham Zoubeir. "Développement en série de fonctions holomorphes des fonctions d'une classe de Gevrey sur l'intervalle [-1;1]." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 287–93. http://dx.doi.org/10.2298/pim141101010b.

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We characterize Gevrey functions on the unit interval [-1; 1] as sums of holomorphic functions in specific neighborhoods of [-1; 1]. As an application of our main theorem, we perform a simple proof for Dyn'kin's theorem of pseudoanalytic extension for Gevrey classes on [-1; 1].

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20

Chaumat, Jacques, and Anne-Marie Chollet. "Propriétés de l'intersection des classes de Gevrey et de certaines autres classes." Bulletin des Sciences Mathématiques 122, no. 6 (October 1998): 455–85. http://dx.doi.org/10.1016/s0007-4497(98)80003-1.

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21

Pilipovic, Stevan, Nenad Teofanov, and Filip Tomic. "Beyond gevrey regularity: Superposition and propagation of singularities." Filomat 32, no. 8 (2018): 2763–82. http://dx.doi.org/10.2298/fil1808763p.

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We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is closed under superposition, and therefore inverse closed as well. Furthermore, we study partial differential operators whose coefficients are less regular then Gevrey-type ultradifferentiable functions. To that aim we introduce appropriate wave front sets and prove a theorem on propagation of singularities. This extends related known results in the sense that assumptions on the regularity of the coefficients are weakened.

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22

Ermine, Jean-Louis. "Développements asymptotiques et microfonctions dans les classes de Gevrey." Publications of the Research Institute for Mathematical Sciences 21, no. 4 (1985): 737–59. http://dx.doi.org/10.2977/prims/1195178927.

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23

SANZ, J. "LINEAR CONTINUOUS EXTENSION OPERATORS FOR GEVREY CLASSES ON POLYSECTORS." Glasgow Mathematical Journal 45, no. 2 (May 2003): 199–216. http://dx.doi.org/10.1017/s0017089503001319.

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24

Liess, Otto. "Microlocality of the cauchy problem in inhomogeneous gevrey classes." Communications in Partial Differential Equations 11, no. 13 (January 1986): 1379–437. http://dx.doi.org/10.1080/03605308608820468.

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25

Taniguchi, Kazuo. "On multi-products of pseudo-differential operators in Gevrey classes and its application to Gevrey hypoellipticity." Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, no. 9 (1985): 291–93. http://dx.doi.org/10.3792/pjaa.61.291.

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26

Stepanets, A. I., A. S. Serdyuk, and A. L. Shidlich. "On relationship between classes of $(\Psi, \overline\upbeta)$ -differentiable functions and Gevrey classes." Ukrainian Mathematical Journal 61, no. 1 (January 2009): 171–77. http://dx.doi.org/10.1007/s11253-009-0189-x.

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27

Ider, Mostefa. "On the superpostition of functions in carleman classes." Bulletin of the Australian Mathematical Society 39, no. 3 (June 1989): 471–76. http://dx.doi.org/10.1017/s0004972700003397.

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In this paper we deal with classes of infinitely differentiable functions known in the literature as Carleman classes. Our main result is a characterisation of those Carleman classes that are closed under superposition. This result enables us to give a complete solution to a problem that has been considered by Gevrey, Cartan and Bang.

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28

Zoubeir, Hicham. "Solvability in Gevrey Classes of Some Nonlinear Fractional Functional Differential Equations." International Journal of Differential Equations 2020 (June 29, 2020): 1–10. http://dx.doi.org/10.1155/2020/3739249.

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Our purpose in this paper is to prove, under some regularity conditions on the data, the solvability in a Gevrey class of bound −1 on the interval −1,1 of a class of nonlinear fractional functional differential equations.

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29

Cicognani, Massimo, and Luisa Zanghirati. "Nonlinear weakly hyperbolic equations with Levi condition in Gevrey classes." Tsukuba Journal of Mathematics 25, no. 1 (June 2001): 85–102. http://dx.doi.org/10.21099/tkbjm/1496164214.

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30

Itoh, Shigeharu. "The cauchy problem for weakly hyperbolic equations in gevrey classes." Communications in Partial Differential Equations 14, no. 1 (January 1989): 27–61. http://dx.doi.org/10.1080/03605308908820590.

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31

Shinkai, Kenzo, and Kazuo Taniguchi. "Fundamental solution for a degenerate hyperbolic operator in Gevrey classes." Publications of the Research Institute for Mathematical Sciences 28, no. 2 (1992): 169–205. http://dx.doi.org/10.2977/prims/1195168661.

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32

Castellanos, Jairo E., Paulo D. Cordaro, and Gerson Petronilho. "Gevrey vectors in involutive tube structures and Gevrey regularity for the solutions of certain classes of semilinear systems." Journal d'Analyse Mathématique 119, no. 1 (April 2013): 333–64. http://dx.doi.org/10.1007/s11854-013-0011-4.

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33

Markin, Marat V. "Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator”." International Journal of Mathematics and Mathematical Sciences 2018 (2018): 1–3. http://dx.doi.org/10.1155/2018/2135740.

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The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space established in “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator,” Int. J. Math. Math. Sci. 2004 (2004), no. 60, 3219–3235, are observed to remain true due to more recent findings.

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34

Komlov, A. V. "Estimates of the Gevrey classes of scattering data for polynomial potentials." Russian Mathematical Surveys 63, no. 4 (August 31, 2008): 788–89. http://dx.doi.org/10.1070/rm2008v063n04abeh004559.

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35

Colombini, F., and J. Rauch. "Sharp Finite Speed for Hyperbolic Problems Well Posed in Gevrey Classes." Communications in Partial Differential Equations 36, no. 1 (January 2011): 1–9. http://dx.doi.org/10.1080/03605302.2010.531859.

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36

Honda, Naofumi. "On the reconstruction theorem of holonomic modules in the Gevrey classes." Publications of the Research Institute for Mathematical Sciences 27, no. 6 (1991): 923–43. http://dx.doi.org/10.2977/prims/1195169005.

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37

Morando, Alessandro. "Hypoellipticity and local solvability of pseudolocal continuous linear operators in Gevrey classes." Tsukuba Journal of Mathematics 28, no. 1 (June 2004): 137–53. http://dx.doi.org/10.21099/tkbjm/1496164718.

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38

Colombini, Ferruccio, and Tatsuo Nishitani. "Systèmes fois fortement hyperboliques dans C∞ et dans les classes de Gevrey." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 330, no. 11 (June 2000): 969–72. http://dx.doi.org/10.1016/s0764-4442(00)00297-4.

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39

Langenbruch, Michael. "Surjectivity of Partial Differential Operators on Gevrey Classes and Extension of Regularity." Mathematische Nachrichten 196, no. 1 (1998): 103–40. http://dx.doi.org/10.1002/mana.19981960106.

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40

Albanese, A. A., and P. Popivanov. "On the global solvability in Gevrey classes on the n-dimensional torus." Journal of Mathematical Analysis and Applications 297, no. 2 (September 2004): 659–72. http://dx.doi.org/10.1016/j.jmaa.2004.04.033.

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41

Kostic, Marko. "Regularization of some classes of ultradistribution semigroups and sines." Publications de l'Institut Math?matique (Belgrade) 87, no. 101 (2010): 9–37. http://dx.doi.org/10.2298/pim1001009k.

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We systematically analyze regularization of different kinds of ultradistribution semigroups and sines, in general, with nondensely defined generators and contemplate several known results concerning the regularization of Gevrey type ultradistribution semigroups. We prove that, for every closed linear operator A which generates an ultradistribution semigroup (sine), there exists a bounded injective operator C such that A generates a global differentiable C-semigroup (C-cosine function) whose derivatives possess some expected properties of operator valued ultradifferentiable functions. With the help of regularized semigroups, we establish the new important characterizations of abstract Beurling spaces associated to nondensely defined generators of ultradistribution semigroups (sines). The study of regularization of ultradistribution sines also enables us to perceive significant ultradifferentiable properties of higher-order abstract Cauchy problems.

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42

Gramchev, Todor V. "The stationary phase method in Gevrey classes and Fourier integral operators on ultradistributions." Banach Center Publications 19, no. 1 (1987): 101–12. http://dx.doi.org/10.4064/-19-1-101-112.

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43

Tahara, Hidetoshi. "Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes." Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, no. 3 (1985): 63–65. http://dx.doi.org/10.3792/pjaa.61.63.

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44

WAKABAYASHI, Seiiehiro. "Singularities of solutions of the Cauchy problem for hyperbolic systems in Gevrey classes." Japanese journal of mathematics. New series 11, no. 1 (1985): 157–201. http://dx.doi.org/10.4099/math1924.11.157.

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45

TAHARA, Hidetoshi. "Singular hyperbolic systems, VI. Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes." Journal of the Mathematical Society of Japan 39, no. 4 (October 1987): 551–80. http://dx.doi.org/10.2969/jmsj/03940551.

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46

Thilliez, Vincent. "Classes de Gevrey non isotropes dans les domaines de type fini de ℂ2." Journal d Analyse Mathematique 60, no. 1 (December 1993): 259–305. http://dx.doi.org/10.1007/bf03341976.

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47

Albanese, A. A., and L. Zanghirati. "Global hypoellipticity and global solvability in Gevrey classes on the n-dimensional torus." Journal of Differential Equations 199, no. 2 (May 2004): 256–68. http://dx.doi.org/10.1016/j.jde.2004.01.005.

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48

Itoh, Shigeharu. "Well-posedness of the Cauchy problem for some weakly hyperbolic operators in Gevrey classes." Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, no. 3 (1985): 66–69. http://dx.doi.org/10.3792/pjaa.61.66.

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49

Li, Qifan. "Local well-posedness for the periodic Korteweg-de Vries equation in analytic Gevrey classes." Communications on Pure & Applied Analysis 11, no. 3 (2012): 1097–109. http://dx.doi.org/10.3934/cpaa.2012.11.1097.

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50

Corli, Andrea. "On local solvability in gevrey classes of linear partial differential operators with multiple characteristics." Communications in Partial Differential Equations 14, no. 1 (January 1989): 1–25. http://dx.doi.org/10.1080/03605308908820589.

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